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Q.

The interference pattern is obtained with two coherent light sources of intensity ratio 4 : 1. And the ratio $\frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}}$ is $\frac{5}{x}$ . Then, the value of x will be equal to :

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a

3

b

4

c

2

d

1

answer is B.

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Detailed Solution

$\frac{I_{1}}{I_{2}} = 4 \frac{I_{\max}}{I_{\min}} = {[\frac{\sqrt{I_{1}} + \sqrt{I_{2}}}{\sqrt{I_{1}} - \sqrt{I_{2}}}]}^{2} \frac{I_{\max}}{I_{\min}} = {[\frac{2 \sqrt{I_{2}} + \sqrt{I_{2}}}{2 \sqrt{I_{2}} - \sqrt{I_{2}}}]}^{2} \frac{I_{\max}}{I_{\min}} = 9 \frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}} = \frac{10}{8} \frac{5}{x} = \frac{10}{8} x = 4$

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